A systematic theoretical investigation of the lowest valence- and Rydberg-excited singlet states of trans-butadiene.: The character of the 11Bu (V) state revisited

In the present work systematic procedures for the balanced description of the lowest singlet excited valence and Rydberg states of butadiene, especially for the correct description of the 1(1)B(u) state, are presented. In the first step of the calculation averaged natural orbitals (ANOs) were computed from the density matrices of the ground state, the 2(1)A(g) and the 1(1)B(u) states. For the 1(1)B(u) state the configuration interaction (CI) wave function used for the computation of the respective density matrix contained all possible single and double excitations from the 1b(g)(pi) orbital into all virtual orbitals and double excitations describing sigma-pi electron correlation. For the ground and 2(1)A(g) states a standard multireference (MR) CI with singles and doubles (CISD)/complete-active-space (CAS)(4,4) wave function was used. In the second step, these ANOs were used in extended MR-CISD, MR-CISD with Davidson correction and MR averaged quadratic coupled cluster calculations. This scheme was also extended to state-averaging including the four lowest Rydberg states 1(1)B(g)(3s), 1(1)A(u)(3p(sigma)), 2(1)A(u)(3p(sigma)) and 2(1)B(u)(3p(pi)). Our best value for the vertical excitation energy to the 1(1)B(u) state is 6.18 eV, close to previous equation-of-motion coupled-cluster with singles and doubles including noniterative triples [EOM - CCSD ((T) over tilde)] and complete-active-space perturbation theory to second order (CASPT2) results, but significantly lower than most of the previous MR-CI and MR-CI based results. The computed vertical excitation energy to the 2(1)A(g) state of 6.55 eV is significantly below previous EOM-CCSD(T) and EOM - CCSD((T) over tilde) results and demonstrates the deficiencies of these methods in the case of MR situations. On the other hand, this excitation energy is larger than previous CASPT2 results for the 2(1)A(g) state. The character of the 1(1)B(u) state is predominantly of valence character, but is more diffuse than the ground state. <x(2)> values for the 1(1)B(u) state range between 25.4 and 26.3a(0)(2) in the three-state calculations.